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Saturday, August 11, 2012

2.Risk Measurement
This involves projecting future prices and rates and using these projections to estimate the risk of loss of the portfolio.
Estimating magnitude of any potential adverse changes in individual risk factors(the volatility of market prices) to allow the quantum of any loss to be estimated.
The inter-relationship of changes between market risk factors (the correlation between risk factors) to allow incorporation of any benefits of diversification of risks within the portfolio.
One technique that permits such a measurement is VaR (Value at Risk).

3.The Value at risk measure
VAR is the loss over N days that will not be exceeded at a X% level of confidence.
VAR is a function of two parameters:
1. N – time horizon in days
2. X – confidence
The two main approaches to calculating VaR:
1. Historical simulation
2. Model–building
In calculating a bank’s capital, banks use N = 10 and X = 99%.
This is the loss level on a 10–day horizon that is expected to be exceeded only 1% of the times.
The capital they require the bank to keep is at least three times this measure.

4.The time horizon

5.Historical VaR
Historical simulation involves using past data as a guide to what might happen in the future.
Suppose that we want to calculate VaR for a portfolio using a one–day time horizon,
99% confidence level and 500 days of data.
1. Identify market variables affecting the portfolio – exchange rates, equity prices, interest rates etc.
2. We collect the movement in these variables over the last 500 days. This provides 500 alternate scenarios between today and tomorrow.
3. We value our portfolio under these 500 alternate scenarios. This provides a probability distribution for daily changes in our portfolio.
4. We rank the scenarios from worst to best. The fifth worst scenario is the first percentile of the distribution. At a 99% confidence level, this is the loss we will incur on a one–day horizon.

6.Think
What is the VaR at 95% level of confidence? Which observation will give us the value of VaR using a data set of 500 days?

7.Our portfolio
• A well diversified portfolio consisting of 50 stocks.
• Three years of daily price data
• Daily prices converted to daily returns
• The returns series is then analysed